Vector fields on Singular Varieties

• Κύριοι συγγραφείς: Brasselet, Jean-Paul (Συγγραφέας), Seade, José (Συγγραφέας), Suwa, Tatsuo (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Σειρά: Lecture Notes in Mathematics, 1987
• Θέματα: Mathematics.; Algebraic geometry.; Dynamics.; Ergodic theory.; Global analysis (Mathematics).; Manifolds (Mathematics).; Functions of complex variables.; Complex manifolds.; Several Complex Variables and Analytic Spaces.; Dynamical Systems and Ergodic Theory.; Manifolds and Cell Complexes (incl. Diff.Topology).; Global Analysis and Analysis on Manifolds.; Algebraic Geometry.
• Φυσική περιγραφή: XX, 232 p. online resource.
• ISBN: 9783642052057
• ISSN: 0075-8434 ;

Vector fields on manifolds play a major role in mathematics and other sciences. In particular, the Poincaré-Hopf index theorem gives rise to the theory of Chern classes, key manifold-invariants in geometry and topology. It is natural to ask what is the ‘good’ notion of the index of a vector field, and of Chern classes, if the underlying space becomes singular. The question has been explored by several authors resulting in various answers, starting with the pioneering work of M.-H. Schwartz and R. MacPherson. We present these notions in the framework of the obstruction theory and the Chern-Weil theory. The interplay between these two methods is one of the main features of the monograph.